Evolutionary Multi-objective Optimization Researchers Research Articles

A Survey on the Hypervolume Indicator in Evolutionary Multiobjective Optimization

Hypervolume is widely used as a performance indicator in the field of evolutionary multiobjective optimization (EMO). It is used not only for performance evaluation of EMO algorithms (EMOAs) but also in indicator-based EMOAs to guide the search. Since its initial proposal in the late 1990s, a wide variety of studies have been done on various topics, including hypervolume calculation, optimal μ-distribution, subset selection, hypervolume-based EMOAs, and extensions of the hypervolume indicator. However, currently there is no work to systematically survey the hypervolume indicator for these topics whereas it has been frequently used in the EMO field. This article aims to fill this gap and provide a comprehensive survey on the hypervolume indicator. We expect that this survey will help EMO researchers to understand the hypervolume indicator more deeply and thoroughly, and promote further utilization of the hypervolume indicator in the EMO field.

NSGA-II With Simple Modification Works Well on a Wide Variety of Many-Objective Problems

In the last two decades, the non-dominated sorting genetic algorithm II (NSGA-II) has been the most widely-used evolutionary multi-objective optimization (EMO) algorithm. However, its performance on a wide variety of many-objective test problems has not been examined in the literature. It has been implicitly assumed by EMO researchers that NSGA-II does not work well on many-objective problems. As a result, NSGA-II has always been excluded from performance comparison with recently proposed many-objective EMO algorithms. Recently, it was pointed out that the performance of NSGA-II on many-objective problems is not always bad. In fact, the poor performance of NSGA-II on many-objective problems is mainly due to the existence of dominance resistant solutions. In this article, we show that the negative effect of the dominance resistant solutions can be remedied by slightly modifying objective values of many-objective problems in NSGA-II. Experimental results show that the modified NSGA-II works well on a wide variety of many-objective test problems.

On Benchmark Problems and Metrics for Decision Space Performance Analysis in Multi-Objective Optimization

A number of benchmark problems exist for evaluating multi-objective evolutionary algorithms (MOEAs) in the objective space. However, the decision space performance analysis is a recent and relatively less explored topic in evolutionary multi-objective optimization research. Among other implications, such analysis can lead to designing more realistic test problems, gaining better understanding about optimal and robust design areas, and design and evaluation of knowledge-based optimization algorithms. This paper complements the existing research in this area and proposes a new method to generate multi-objective optimization test problems with clustered Pareto sets in hyper-rectangular defined areas of decision space. The test problem is parametrized to control number of decision variables, number and position of optimal areas in the decision space and modality of fitness landscape. Three leading MOEAs, including NSGA-II, NSGA-III, and MOEA/D, are evaluated on a number of problem instances with varying characteristics. A new metric is proposed that measures the performance of algorithms in terms of their coverage of the optimal areas in the decision space. The empirical analysis presented in this research shows that the decision space performance may not necessarily be reflective of the objective space performance and that all algorithms are sensitive to population size parameter for the new test problems.

Current trends in evolutionary multi-objective optimization

In a short span of about 14 years, evolutionary multi-objective optimization (EMO) has established itself as a mature field of research and application with an extensive literature, many commercial softwares, numerous freely downloadable codes, a dedicated biannual conference running successfully four times so far since 2001, special sessions and workshops held at all major evolutionary computing conferences, and full-time researchers from universities and industries from all around the globe. In this paper, we make a brief outline of EMO principles, some EMO algorithms, and focus on current research and application potential of EMO. Besides, simply finding a set of Pareto-optimal solutions, EMO research has now diversified in hybridizing its search with multi-criterion decision-making tools to arrive at a single preferred solution, in utilizing EMO principle in solving different kinds of single-objective optimization problems efficiently, and in various interesting application domains which were not possible to be solved adequately due to the lack of a suitable solution technique.